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Minimum input for GroebnerBasis

• To: mathgroup at smc.vnet.net
• Subject: [mg90388] Minimum input for GroebnerBasis
• From: TuesdayShopping <TuesdayShopping at yahoo.com>
• Date: Tue, 8 Jul 2008 02:25:29 -0400 (EDT)

Given a finite set of polynomials P in variables belonging to V, we compute the GroebnerBasis G. What is the set of polynomials Q (Q is a subset of P), such that (a) Q produces the same GroebnerBasis G; and, (b) if any element from the set Q is removed, Q will no longer produce G. In other words, Q is the minimum set of polynomials (from P) required, in order to produce the Groebner Basis G. If there are several Q's possible, we will want the one with the smallest number of polynomials in in it. If there are several with the same number, will want the first one we encounter. Question is how do we find Q in Mathematica?

For example, P can be {x + y + 1, 2 x + 2 y + 2, x - y}

GroebnerBasis[{x + y + 1, 2 x + 2 y + 2, x - y}, {x,y}] is {1 + 2 y, 1 + 2 x}

Q is {x + y + 1, x - y}

• Follow-Ups:
  • Re: Minimum input for GroebnerBasis
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Minimum input for GroebnerBasis
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>